Lecture 12

# This is a very important system and is sometimes

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Unformatted text preview: llel servers. I.e., the buffer size is the same as the number of servers; thus, if all the servers are occupied, then an arriving customer is rejected. This is the case in the telephone network link model - if all the circuits are busy, an arriving call is rejected (instead of being queued up if one of them become free later). This is a very important system and is sometimes known as the loss system. The state-transition diagram is λ 0 1 µ 3 2 2µ • j =  if 0  0 j =  j • • (m–1)µ 3µ Here, In this case, λ λ λ m–1 m mµ j m,1 otherwise. if 1  0 jm otherwise. j = =j j1! 0 j = 1 ::: m: Since sum of probabilities is 1, we can show that 2m 3,1 X =j 5 0 = 4 : j! j =0 Speciﬁcally, the probability of an arriving call being blocked is the probability of being in state m: =m m! m =j j =0 j ! m = P : This is the well-known Erlang-B Blocking/loss formula and is usually denoted by E = we wrote m. Further, a = = to denote the offered load in Erlang (this is NOT utilization) giving us: E a m = CS 522, v 0.94, d.medhi, W’99 am m Pm ! aj : j =0 j ! 19 The average number in the system, N , is given by N = a1 , E a m: It is interesting to note that the Erlang-B loss formual has the following recurrence relation: with the starting point B a 0 = 1: a , E a m = m aEaE...
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## This document was uploaded on 03/19/2014 for the course CS 6030 at Western Michigan.

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